Equation Word Problems

Grade 7 · algebra · 90 practice problems · read aloud

🔊 Listen to this explanation

Solving Equation Word Problems

🧠 What is it and Why is it Useful?

Equation word problems take a real-world situation and turn it into a math sentence (an equation) to find an unknown value. This is super useful because it helps you solve everyday problems, like figuring out how many items you can buy with your money or how fast you need to go to be on time.

📝 Step-by-Step Guide

  1. Read Carefully: Understand the problem. What is being asked?
  2. Define the Variable: Choose a letter (like n or x) to represent the unknown number.
  3. Write the Equation: Translate the words into a mathematical equation.
  4. Solve the Equation: Use inverse operations (like subtraction or division) to find the value of your variable.
  5. Check Your Answer: Plug your solution back into the original story. Does it make sense?

🔍 Visual Examples

Example 1: The Birthday Party

You have $48 to spend on pizza for your party. Each pizza costs $12. How many pizzas can you buy?

  1. Variable: Let p = number of pizzas.
  2. Equation: 12p = 48 (cost per pizza times number of pizzas equals total cost)
  3. Solve: 12p = 48 → p = 48 ÷ 12 → p = 4
  4. Check: 4 pizzas × $12 = $48. ✔️

Example 2: Age Problem

Maria is 15 years old. She is 3 years older than twice her brother's age. How old is her brother?

  1. Variable: Let b = brother's age.
  2. Equation: 15 = 2b + 3 (Maria's age is equal to twice her brother's age plus 3)
  3. Solve: 15 - 3 = 2b → 12 = 2b → b = 12 ÷ 2 → b = 6
  4. Check: Twice 6 is 12, plus 3 is 15. ✔️

⚠️ Common Mistakes

  • Misreading the problem: Rushing leads to wrong equations. Tip: Underline key numbers and phrases.
  • Incorrect operation order: Forgetting PEMDAS. In "three more than twice a number," you multiply before adding (2x + 3).
  • Forgetting to check: Your answer might solve the equation but not make sense in the story (like a negative age).

💡 Tips & Tricks

  • Look for key words: "total" often means equals (=), "more than" means add (+), "times" means multiply (×).
  • Draw a picture or diagram to help you visualize the problem.
  • If you get a fraction or decimal, double-check your work—it might still be correct!

🎯 Practice Suggestions

Start with simple problems and gradually try more complex ones.

  • Create your own word problems about your hobbies or allowance.
  • Practice with a friend and explain your steps to each other.
  • Use online math games or worksheets focused on one-step and two-step equations.

Practice problems

6 of the 90, worked through step by step — try them before opening the answer.

1 (-4)³ ÷ 8 + 5 × (3 - 7) = ?

Hint: Remember to follow the order of operations: parentheses first, then exponents, then multiplication and division from left to right, and finally addition and subtraction.

Show the answer

Answer: -28

  1. Solve inside the parentheses: (3 - 7) = -4
  2. Calculate the exponent: (-4)³ = -4 × -4 × -4 = -64
  3. Perform division: -64 ÷ 8 = -8
  4. Perform multiplication: 5 × (-4) = -20
  5. Add the results: -8 + (-20) = -28 The final answer is -28.

2 (-2)³ + 5 × (3 - 7)² ÷ 4 = ?

Hint: Remember to follow the order of operations: parentheses first, then exponents, then multiplication and division from left to right, and finally addition and subtraction.

Show the answer

Answer: 12

  1. Calculate inside the parentheses: (3 - 7) = -4
  2. Apply the exponents: (-2)³ = -8 and (-4)² = 16
  3. Perform multiplication and division from left to right: 5 × 16 = 80, then 80 ÷ 4 = 20
  4. Perform addition: -8 + 20 = 12

The answer is 12.

3 (3/4 + 1/6) ÷ (2/3 - 1/2) = ?

Hint: First find common denominators for the fractions in both parentheses before performing the division operation.

Show the answer

Answer: 11/2

  1. Simplify the numerator (3/4 + 1/6)** To add fractions, find a common denominator. The denominators are 4 and 6. The least common multiple is 12. 3/4 = (3 × 3)/(4 × 3) = 9/12 1/6 = (1 × 2)/(6 × 2) = 2/12 So: 9/12 + 2/12 = 11/12 Numerator = 11/12 --- **
  2. Simplify the denominator (2/3 - 1/2)** Common denominator for 3 and 2 is 6. 2/3 = (2 × 2)/(3 × 2) = 4/6 1/2 = (1 × 3)/(2 × 3) = 3/6 So: 4/6 - 3/6 = 1/6 Denominator = 1/6 --- **
  3. Divide the two results** (11/12) ÷ (1/6) = 11/12 × 6/1 Multiply numerators: 11 × 6 = 66 Multiply denominators: 12 × 1 = 12 So: 66/12 --- **
  4. Simplify 66/12** Both divisible by 6: 66 ÷ 6 = 11 12 ÷ 6 = 2 So: 11/2 --- **Final answer:** 11/2

Let's solve step by step. We have: (3/4 + 1/6) ÷ (2/3 - 1/2) --- **

4 (-4)³ + 2 × (15 - 7)² ÷ 4 = ?

Hint: Remember to follow the order of operations: parentheses first, then exponents, then multiplication and division from left to right, and finally addition and subtraction.

Show the answer

Answer: -32

  1. Evaluate inside the parentheses: (15 - 7) = 8
  2. Calculate the exponents: (-4)³ = -4 × -4 × -4 = -64 and (8)² = 64
  3. Perform multiplication and division from left to right: 2 × 64 = 128, then 128 ÷ 4 = 32
  4. Perform the addition: -64 + 32 = -32

The answer is -32.

5 (-4)³ + 2 × (8 - 12) ÷ (-2) = ?

Hint: Remember to follow the order of operations (PEMDAS) and be careful with negative signs when working with exponents and division.

Show the answer

Answer: -60

  1. Calculate the exponent: (-4)³ = -4 × -4 × -4 = 16 × -4 = -64
  2. Simplify inside parentheses: (8 - 12) = -4
  3. Perform multiplication and division from left to right: 2 × (-4) = -8
  4. Continue division: -8 ÷ (-2) = 4
  5. Add the results: -64 + 4 = -60

The answer is -60.

6 (-5)² + 3 × (8 - 12) ÷ (-2) = ?

Hint: Remember to follow the order of operations (PEMDAS/BODMAS) and pay attention to negative signs when squaring numbers.

Show the answer

Answer: 31

  1. Evaluate the exponent: (-5)² = 25
  2. Calculate inside parentheses: (8 - 12) = -4
  3. Perform multiplication and division from left to right: 3 × (-4) = -12
  4. Continue division: -12 ÷ (-2) = 6
  5. Add the results: 25 + 6 = 31

The answer is 31.

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